Frequency distribution table

Frequency Distribution Table

Afrequency distribution table is a statistical tool used to organize and summarize a set of data. It displays the frequency, or count, of each distinct value or range of values (known as "classes" or "bins") in a dataset. This table is fundamental in descriptive statistics and is often used to provide a visual representation of data, making it easier to identify patterns, trends, and outliers.

Structure of a Frequency Distribution Table

A frequency distribution table typically consists of the following columns:

• Class Interval: This column lists the range of values that the data is divided into. For continuous data, these are often equal-width intervals.
• Frequency: This column shows the number of data points that fall within each class interval.
• Cumulative Frequency: This optional column displays the cumulative total of frequencies up to the current class interval.
• Relative Frequency: This optional column shows the proportion of the total number of data points that fall within each class interval, often expressed as a percentage.

Types of Frequency Distribution

Frequency distribution tables can be categorized based on the type of data:

• Discrete Frequency Distribution: Used for discrete data, where the data can only take specific values (e.g., number of students in a class).
• Continuous Frequency Distribution: Used for continuous data, where the data can take any value within a range (e.g., height, weight).

Steps to Construct a Frequency Distribution Table

1.Collect and Organize Data: Gather the raw data that needs to be analyzed. 2.Determine the Range: Calculate the range of the data by subtracting the smallest value from the largest value. 3.Select the Number of Classes: Decide on the number of class intervals. A common rule of thumb is to use between 5 and 20 classes. 4.Calculate Class Width: Divide the range by the number of classes to determine the class width. Round up to a convenient number if necessary. 5.Create Class Intervals: List the class intervals starting from the smallest data value. 6.Tally the Frequencies: Count the number of data points that fall into each class interval and record these counts in the frequency column.

Example

Consider a dataset representing the ages of 30 students in a class:

| Age Range | Frequency | |-----------|-----------| | 10-14 | 5 | | 15-19 | 12 | | 20-24 | 8 | | 25-29 | 3 | | 30-34 | 2 |

In this example, the class intervals are 5 years wide, and the frequency column shows how many students fall into each age range.

Applications

Frequency distribution tables are widely used in various fields such as:

• Education: To analyze test scores and grades.
• Healthcare: To study the distribution of patient ages, blood pressure readings, etc.
• Business: To assess sales data, customer demographics, etc.

Also see

• Histogram
• Bar chart
• Descriptive statistics
• Probability distribution